Constructions of Given-Depth and Optimal Multirate Rearrangeably Nonblocking Distributors

The theory of multirate switching networks, started in the late 80s, has been very practically useful. In particular, it has served as the theoretical foundation for the development of most ATM switching systems. Rearrangeable multirate multicast switching networks are customarily called distribution networks, or distributors for short. It has been known for more than 15 years that distributors with cross-point complexity O(n log² n) can be constructed, where n is the number of inputs. The problem of constructing optimal distributors remains open thus far. In this paper, we give a general method for constructing given-depth rearrangeable multirate distributors. One of the rewards of our construction method is a distributor with cross-point complexity O(n log n), which we then show to be optimal. We thus settle the aforementioned open problem.